Problem: Express this product in scientific notation: $(4.00\times 10^{-1})\times (9.00\times 10^{2})$
Explanation: Start by collecting like terms together. $= (4.00\times 9.00) \times (10^{-1}\times 10^{2})$ When multiplying exponents with the same base, add the powers together. $= 36.0 \times 10^{-1\,+\,2}$ $= 36.0 \times 10^{1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $36.0$ is the same as $3.600 \times 10$ $ = {3.600 \times 10} \times 10^{1} $ $= 3.600\times 10^{2}$